That last survey was linked, by the Department of Education, to an article in the Telegraph, rather than the initial survey.

To be clear, five of the six "surveys" cited by the Department of Education in backing up a claim by a cabinet minister were PR-commissioned puff-polls. They were commissioned, not to find out information in a trustworthy and repeatable manner, but to ensure that stories about UKTV Gold, Premier Inn, the Sea Cadets , Bomber Command Memorial and "teacher-set exam revision service" Education Quizzes found their way into UK papers. Some of them may additionally be respectable polling – the Lord Ashcroft poll around Bomber Memorial Command uses a nationally representative sample, non-leading questions, and face-to-face interviews, for instance – but it's the sort of thing which normally rings alarm bells.

The last cited survey isn't a survey. It's a pamphlet on "Freedom, Aspiration and the New Curriculum" from think-tank Politeia. While it agrees with Gove's conclusion, it is hardly a primary source (an ironic distinction to have to make in a discussion about history teaching).

If this the sort of information which is revealed when the Department of Education responds to freedom of information requests, it's becoming clearer why they so rarely do it.